Inhalt

The lectures cover major ideas of complex network theory, with emphasis on nonlinear dynamics and applications in real-world systems. A focus is put on characterization of emergent collective behavior when the network nodes are coupled over various configurations, including the Kuramoto model of coupled phase oscillators and coupled chaotic maps. Conditions for different types of synchronization and clustering will be derived with combination of analytical methods and numerical simulations. The main attention will be paid to chimera states as one of the most fascinating recent discoveries in nonlinear science, illuminating self-organized spatial coexistence of synchronization and desynchronization. Experimental evidence of chimera states will be presented for such fields as neuroscience, chemistry, optics, fluid dynamics, and mechanical systems.

More specifically, the following topics will be discussed in the lectures:

Synchronization in complex networks, theory and application

Nonlinear dynamics, bifurcations and chaos

Kuramoto model: collective dynamics and phase chaos

Chaotic synchronization, riddling and blowout bifurcations

Chimera states as a new paradigm of network science

Different types of chimera states in Kuramoto, FitzHugh-Nagumo and coupled map models

Kuramoto model with inertia, solitary states and spatial chaos

Self-propelled chimeras in the Vicsek model

Chimera states in delayed-feedback systems

Chimera states in 2 and 3 spatial dimensions: spiral and scroll wave chimeras